Physics

Raymond A. Serway, Jerry S. Faughn

Chapter 13 Light and Reflection - all with Video Answers

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Chapter Questions

01:08

Problem 1

Which band of the electromagnetic spectrum has
a. the lowest frequency?
b. the shortest wavelength?

Matt Braby

Numerade Educator

02:18

Problem 2

Which of the following electromagnetic waves has the highest frequency?
a. radio
b. ultraviolet radiation
c. blue light
d. infrared radiation

Jacob Adamczyk

Numerade Educator

00:39

Problem 3

Why can light be used to measure distances accurately? What must be known in order to make distance measurements?

Matt Braby

Numerade Educator

01:40

For the diagram below, use Huygens' principle to show what the wave front at point $A$ will look like at point $B$. How would you represent this wave front in the ray approximation?
(FIGURE CANT COPY)

Khoobchandra Agrawal

Numerade Educator

00:50

Problem 5

What is the relationship between the actual brightness of a light source and its apparent brightness from where you see it?

Matt Braby

Numerade Educator

01:32

Problem 6

Suppose an intelligent society capable of receiving and transmitting radio signals lives on a planet orbiting Procyon, a star 95 light-years away from Earth. If a signal were sent toward Procyon in 1999 what is the earliest year that Earth could expect to receive a return message? (Hint: A light-year is the distance a ray of light travels in one year.)

Jacob Adamczyk

Numerade Educator

00:18

Problem 7

How fast do X rays travel in a vacuum?

Matt Braby

Numerade Educator

01:12

Problem 8

Why do astronomers observing distant galaxies talk about looking backward in time?

Jacob Adamczyk

Numerade Educator

00:54

Problem 9

Do the brightest stars that you see in the night sky necessarily give off more light than dimmer stars? Explain your answer.

Matt Braby

Numerade Educator

02:13

Problem 10

See Sample Problem A
The compound eyes of bees and other insects are highly sensitive to light in the ultraviolet portion of the spectrum, particularly light with frequencies between $7.5 \times 10^{14} \mathrm{Hz}$ and $1.0 \times 10^{15} \mathrm{Hz} .$ To what wavelengths do these frequencies correspond?

Supratim Pal

Numerade Educator

01:12

Problem 11

The brightest light detected from the star Antares has a frequency of about $3 \times 10^{14} \mathrm{Hz}$. What is the wavelength of this light?

Matt Braby

Numerade Educator

02:40

Problem 12

What is the wavelength for an FM radio signal if the number on the dial reads $99.5 \mathrm{MHz} ?$

Jacob Adamczyk

Numerade Educator

01:48

Problem 13

What is the wavelength of a radar signal that has a frequency of $33 \mathrm{GHz} ?$

Matt Braby

Numerade Educator

03:29

Problem 14

For each of the objects listed below, identify whether light is reflected diffusely or specularly.
a. a concrete driveway
b. an undisturbed pond
c. a polished silver tray
d. a sheet of paper
e. a mercury column in a thermometer

Jacob Adamczyk

Numerade Educator

01:19

Problem 15

If you are stranded on an island, where would you align a mirror to use sunlight to signal a searching aircraft?

Matt Braby

Numerade Educator

01:33

Problem 16

If you are standing $2 \mathrm{m}$ in front of a flat mirror, how far behind the mirror is your image? What is the magnification of the image?

Jacob Adamczyk

Numerade Educator

01:31

Problem 17

When you shine a flashlight across a room, you see the beam of light on the wall. Why do you not see the light in the air?

Matt Braby

Numerade Educator

02:59

Problem 18

How can an object be a specular reflector for some electromagnetic waves yet be diffuse for others?

Jacob Adamczyk

Numerade Educator

01:42

Problem 19

A flat mirror that is $0.85 \mathrm{m}$ tall is attached to a wall so that its upper edge is $1.7 \mathrm{m}$ above the floor. Use the law of reflection and a ray diagram to determine if this mirror will show a person who is 1.7 m tall his or her complete reflection.

Matt Braby

Numerade Educator

03:31

Problem 20

Two flat mirrors make an angle of $90.0^{\circ}$ with each other, as diagrammed at right. An incoming ray makes an angle of $35^{\circ}$ with the normal of mirror $A$
Use the law of reflection to determine the angle of reflection from mirror $\mathrm{B}$. What is unusual about the incoming and reflected rays of light for this arrangement of mirrors?

Jacob Adamczyk

Numerade Educator

02:00

Problem 20

Two flat mirrors make an angle of $90.0^{\circ}$ with each other, as diagrammed at right. An incoming ray makes an angle of $35^{\circ}$ with the normal of mirror $\mathrm{A}$.
Use the law of reflection to determine the angle of reflection from mirror B. What is unusual about the incoming and reflected rays of light for this arrangement of mirrors?
(FIGURE CANT COPY)

Keshav Singh

Numerade Educator

00:40

Problem 21

If you walk $1.2 \mathrm{m} / \mathrm{s}$ toward a flat mirror, how fast does your image move with respect to the mirror? In what direction does your image move with respect to you?

Matt Braby

Numerade Educator

01:52

Problem 22

If you walk $1.2 \mathrm{m} / \mathrm{s}$ toward a flat mirror, how fast does your image move with respect to the mirror? In what direction does your image move with respect to you?

Jacob Adamczyk

Numerade Educator

00:30

Problem 23

Which type of mirror should be used to project movie images on a large screen?

Matt Braby

Numerade Educator

01:18

Problem 24

If an object is placed outside the focal length of a concave mirror, which type of image will be formed? Will it appear in front of or behind the mirror?

Jacob Adamczyk

Numerade Educator

00:40

Problem 25

Can you use a convex mirror to burn a hole in paper by focusing light rays from the sun at the mirror's focal point?

Matt Braby

Numerade Educator

07:23

Problem 26

A convex mirror forms an image from a real object. Can the image ever be larger than the object?

Khoobchandra Agrawal

Numerade Educator

01:27

Problem 27

Why are parabolic mirrors preferred over spherical concave mirrors for use in reflecting telescopes?

Matt Braby

Numerade Educator

00:41

Problem 28

Where does a ray of light that is parallel to the principal axis of a concave mirror go after it is reflected at the mirror's surface?

Jacob Adamczyk

Numerade Educator

01:04

Problem 29

What happens to the real image produced by a concave mirror if you move the original object to the location of the image?

Matt Braby

Numerade Educator

04:33

Problem 30

Consider a concave spherical mirror and a real object. Is the image always inverted? Is the image always real? Give conditions for your answers.

Jacob Adamczyk

Numerade Educator

00:52

Problem 31

Explain why enlarged images seem dimmer than the original objects.

Matt Braby

Numerade Educator

00:39

Problem 32

What test could you perform to determine if an image is real or virtual?

Jacob Adamczyk

Numerade Educator

00:59

Problem 33

You've been given a concave mirror that may or may not be parabolic. What test could you perform to determine whether it is parabolic?

Matt Braby

Numerade Educator

09:28

Problem 34

A concave shaving mirror has a radius of curvature of $25.0 \mathrm{cm} .$ For each of the following cases, find the magnification, and determine whether the image formed is real or virtual and upright or inverted.
a. an upright pencil placed $45.0 \mathrm{cm}$ from the mirror
b. an upright pencil placed $25.0 \mathrm{cm}$ from the mirror
c. an upright pencil placed $5.00 \mathrm{cm}$ from the mirror

Meghan Miholics

Numerade Educator

03:33

Problem 35

A concave spherical mirror can be used to project an image onto a sheet of paper, allowing the magnified image of an illuminated real object to be accurately traced. If you have a concave mirror with a focal length of $8.5 \mathrm{cm},$ where would you place a sheet of paper so that the image projected onto it is twice as far from the mirror as the object is? Is the image upright or inverted, real or virtual? What would the magnification of the image be?

Vishal Gupta

Numerade Educator

05:26

Problem 36

A convex mirror with a radius of curvature of $45.0 \mathrm{cm}$ forms a $1.70 \mathrm{cm}$ tall image of a pencil at a distance of $15.8 \mathrm{cm}$ behind the mirror. Calculate the object distance for the pencil and its height. Is the image real or virtual? What is the magnification? Is the image inverted or upright?

Jacob Adamczyk

Numerade Educator

00:43

Problem 37

What are the three primary additive colors? What happens when you mix them?

Matt Braby

Numerade Educator

00:37

Problem 38

What are the three primary subtractive colors (or primary pigments)? What happens when you mix them?

Jacob Adamczyk

Numerade Educator

00:59

Problem 39

Explain why a polarizing disk used to analyze light can block light from a beam that has been passed through another polarizer. What is the relative orientation of the two polarizing disks?

Matt Braby

Numerade Educator

03:21

Problem 40

Explain what could happen when you mix the following:
a. cyan and yellow pigment
b. blue and yellow light
c. pure blue and pure yellow pigment
d. green and red light
e. green and blue light

Khoobchandra Agrawal

Numerade Educator

01:49

Problem 41

What color would an opaque magenta shirt appear
to be under the following colors of light?
a. white
d. green
b. red
e. yellow
c. cyan

Matt Braby

Numerade Educator

01:03

Problem 42

A substance is known to reflect green and blue light. What color would it appear to be when it is illuminated by white light? by blue light?

Jacob Adamczyk

Numerade Educator

00:49

Problem 43

How can you tell if a pair of sunglasses has polarizing lenses?

Matt Braby

Numerade Educator

02:03

Problem 44

Why would sunglasses with polarizing lenses remove the glare from your view of the hood of your car or a distant body of water but not from a tall metal tank used for storing liquids?

Jacob Adamczyk

Numerade Educator

00:56

Problem 45

Is light from the sky polarized? Why do clouds seen through polarizing glasses stand out in bold contrast to the sky?

Matt Braby

Numerade Educator

03:10

Problem 46

The real image of a tree is magnified -0.085 times by a telescope's primary mirror. If the tree's image forms $35 \mathrm{cm}$ in front of the mirror, what is the distance between the mirror and the tree? What is the
focal length of the mirror? What is the value for the mirror's radius of curvature? Is the image virtual or real? Is the image inverted or upright?

Jacob Adamczyk

Numerade Educator

02:49

Problem 47

A candlestick holder has a concave reflector behind the candle, as shown below. The reflector magnifies a candle -0.75 times and forms an image $4.6 \mathrm{cm}$ away from the reflector's surface. Is the image inverted or upright? What are the object distance and the reflector's focal length? Is the image virtual or real?

Matt Braby

Numerade Educator

04:40

Problem 48

A child holds a candy bar $15.5 \mathrm{cm}$ in front of the convex side-view mirror of an automobile. The image height is reduced by one-half. What is the radius of curvature of the mirror?

Jacob Adamczyk

Numerade Educator

03:05

Problem 49

A glowing electric light bulb placed $15 \mathrm{cm}$ from a concave spherical mirror produces a real image $8.5 \mathrm{cm}$ from the mirror. If the light bulb is moved to a position $25 \mathrm{cm}$ from the mirror, what is the position of the image? Is the final image real or virtual? What are the magnifications of the first and final images? Are the two images inverted or upright?

Matt Braby

Numerade Educator

03:56

Problem 50

A convex mirror is placed on the ceiling at the intersection of two hallways. If a person stands directly underneath the mirror, the person's shoe is a distance of $195 \mathrm{cm}$ from the mirror. The mirror forms an image of the shoe that appears $12.8 \mathrm{cm}$ behind the mirror's surface. What is the mirror's focal length? What is the magnification of the image? Is the image real or virtual? Is the image upright or inverted?

Khoobchandra Agrawal

Numerade Educator

02:23

Problem 51

The side-view mirror of an automobile has a radius of curvature of $11.3 \mathrm{cm} .$ The mirror produces a virtual image one-third the size of the object. How far is the object from the mirror?

Matt Braby

Numerade Educator

01:56

Problem 52

An object is placed $10.0 \mathrm{cm}$ in front of a mirror. What type must the mirror be to form an image of the object on a wall $2.00 \mathrm{m}$ away from the mirror? What is the magnification of the image? Is the image real or virtual? Is the image inverted or upright?

Khoobchandra Agrawal

Numerade Educator

03:46

Problem 53

The reflecting surfaces of two intersecting flat mirrors are at an angle of $\theta\left(0^{\circ}<\theta<90^{\circ}\right),$ as shown in the figure below. A light ray strikes the horizontal mirror. Use the law of reflection to show that the emerging ray will intersect the incident ray at an angle of $\phi=180^{\circ}-2 \theta$

Matt Braby

Numerade Educator

02:33

Problem 54

Show that if a flat mirror is assumed to have an "infinite" radius of curvature, the mirror equation reduces to $q=-p$

Jacob Adamczyk

Numerade Educator

02:24

Problem 55

A real object is placed at the zero end of a meterstick. A large concave mirror at the $100.0 \mathrm{cm}$ end of the meterstick forms an image of the object at the $70.0 \mathrm{cm}$ position. A small convex mirror placed at the $20.0 \mathrm{cm}$ position forms a final image at the $10.0 \mathrm{cm}$ point. What is the radius of curvature of the convex mirror? (Hint: The first image created by the concave mirror acts as an object for the convex mirror.)

Matt Braby

Numerade Educator

05:57

Problem 56

A dedicated sports-car enthusiast polishes the inside and outside surfaces of a hubcap that is a section of a sphere. When he looks into one side of the hubcap, he sees an image of his face $30.0 \mathrm{cm}$ behind the hubcap. He then turns the hubcap over and sees another image of his face $10.0 \mathrm{cm}$ behind the hubcap.
a. How far is his face from the hubcap?
b. What is the radius of curvature of the hubcap?
c. What is the magnification for each image?
d. Are the images real or virtual?
e. Are the images upright or inverted?

Khoobchandra Agrawal

Numerade Educator

02:22

Problem 57

An object $2.70 \mathrm{cm}$ tall is placed $12.0 \mathrm{cm}$ in front of a mirror. What type of mirror and what radius of curvature are needed to create an upright image that is $5.40 \mathrm{cm}$ in height? What is the magnification of the image? Is the image real or virtual?

Matt Braby

Numerade Educator

06:11

Problem 58

A "floating coin" illusion consists of two parabolic mirrors, each with a focal length of $7.5 \mathrm{cm},$ facing each other so that their centers are $7.5 \mathrm{cm}$ apart (see the figure below). If a few coins are placed on the lower mirror, an image of the coins forms in the small opening at the center of the top mirror. Use the mirror equation, and draw a ray diagram to show that the final image forms at that location. Show that the magnification is 1 and that the image is real and upright. (Note: A flashlight beam shined on these images has a very startling effect. Even at a glancing angle, the incoming light beam is seemingly reflected off the images of the coins. Do you understand why?)
(FIGURE CANT COPY)

Khoobchandra Agrawal

Numerade Educator

03:02

Problem 59

Use the mirror equation and the equation for magnification to prove that the image of a real object formed by a convex mirror is always upright, virtual, and smaller than the object. Use the same equations to prove that the image of a real object placed in front of any spherical mirror is always virtual and upright when $p<|f|$

Matt Braby

Numerade Educator

07:35

Problem 60

Use trigonometry to derive the mirror and magnification equations. (Hint: Note that the incoming ray between the object and the mirror forms the hypotenuse of a right triangle. The reflected ray between the image point and the mirror is also the hypotenuse of a right triangle.)

Khoobchandra Agrawal

Numerade Educator